Macroeconomic Interdependence in a Two-Country DSGE Model under Diverging Interest-Rate Rules



3. New Open Economy Macroeconomic Model

domestic currency and are supposed to be internationally tradable.14

Money holdings Mt-1 can also be transferred from t - 1 to t but yield no nominal return. Consumption
goods, however, are perishable and cannot be stored. Γ
t(h) are instantaneous profits of the representative
household acting as a producer of an individual, differentiated domestic good
h, which will be explained
in more detail below. Finally, let
τ denote non-distortionary real lump-sum taxes.

Again, for the representative foreign household the intertemporal budget constraint is the same as (17).
Since internationally traded bonds are supposed to be denominated in domestic currency, foreign bond
holdings in domestic currency
B* first have to be divided by the nominal exchange rate before they enter
the foreign intertemporal budget constraint:
B*/S. Moreover, W * may differ from W, i* from i, Γ * ( f )
from Γ(
h), as well as τ * from τ .

The maximization of the utility function (1) subject to the budget constraint (17) then holding with
equality is undertaken by maximizing the corresponding Lagrangian and yields the subsequent first order
conditions for a utility maximum:

C-ρ

—= β (1 + it ) Et
Pt


-ρ

Ct +1


Pt+1


(18)


This is the intertemporal Euler equation for total real consumption stating that the marginal rate of
substitution between total real consumption in
t and in t + 1 equals their discounted relative prices.

Moreover, one obtains that in a utility maximum the marginal rate of substitution between real money
balances and total real consumption equals the opportunity costs of holding money:

-ε

Mt

Pt J    = it

(19)


C-ρ   1 1 + it '

Note that equation (19) can be rearranged in order to get the following money demand equation:

/W = γ1+2t c ρ

pt) χ it Ct,
where one can see that the higher total real consumption, the higher is demand for real money balances.

Finally, one also gets the subsequent labor supply equation:

L-ξ = W.
γc
-ρ   Pt ,

(20)


which states that the marginal rate of substitution between labor and total real consumption equals their
relative prices, the real consumer wage. For a derivation of conditions (18), (19), and (20) see Appendix

A.2.

Note that analogous equations to (18), (19), and (20) also hold abroad.

3.3. Firms

Let us assume further that agents at home and abroad do not only act as utility maximizing households,
but also as profit maximizing firms of final goods, which shall be producible without the input of inter-
mediate goods. In contrast to their role as households whose preferences are assumed to be identical, all
commodities are differentiated goods satisfying the households’ love of variety.

Hence, there is the possibility to raise individual goods’ prices, p (h), p(f), above marginal cost without

14 Note that one could generalize this formulation by assuming that domestic and foreign households had access to a complete
portfolio of state-contingent Arrow-Debreu securities, both domestically and internationally tradable, as in Clarida et
al. (2002) in order to guarantee for the completeness of (international) financial markets.



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